Asymptotic Behavior For A Degenerate Parabolic System Coupled Via Non-local Sources

This Thesis deals with asymptotic behavior of solutions to a degenerate parabolic system coupled via nonlinear non-local sources, such as critical exponents, blow-up rate, blow-up profile near the blow-up time, etc. We will introduce different linear algebraic systems to describe the critical exponents and the asymptotic behavior of solutions, respectively.In the introduction, we give the background to the study of nonlinear parabolic equations. In Chapter 2, we state some primary tools related to this paper. In Chapter 3, we show the local existence of classical solutions for the transformed system. In Chapter 4, we firstly introduce the so called characteristic algebraic systems describing the critical exponents. In Chapter 5, we establish the blow-up rate and profile for the problem. Finally, in the last chapter, we give some remarks on the conclusions obtained in this paper.